General Overview of Conventional Image-compression Techniques
To help the reader more easily understand the concepts discussed below in the description of the invention, following is a basic overview of conventional image-compression techniques.
To electronically transmit a relatively high-resolution image over a relatively low-band-width channel, or to electronically store such an image in a relatively small memory space, it is often necessary to compress the digital data that represents the image. Such image compression typically involves reducing the number of data bits necessary to represent an image. For example, High-Definition-Television (HDTV) video images are compressed to allow their transmission over existing television channels. Without compression, HDTV video images would require transmission channels having bandwidths much greater than the bandwidths of existing television channels. Furthermore, to reduce data traffic and transmission time to acceptable levels, an image may be compressed before being sent over the internet. Or, to increase the image-storage capacity of a CD-ROM or server, an image may be compressed before being stored thereon.
Referring to FIGS. 1A–7, the basics of the popular block-based Moving Pictures Experts Group (MPEG) compression standards, which include MPEG-1, MPEG-2, and MPEG-4 are discussed. For purposes of illustration, the discussion is based on using an MPEG 4:2:0 format to compress video images represented in a Y, CB, CR color space. However, the discussed concepts also apply to other MPEG formats, to images that are represented in other color spaces, and to other block-based compression standards such as the Joint Photographic Experts Group (JPEG) standard, which is often used to compress still images. Furthermore, although many details of the MPEG standards and the Y, CB, CR color space are omitted for brevity, these details are well known and are disclosed in a large number of available references.
Still referring to FIGS. 1A–7, the MPEG standards are often used to compress temporal sequences of images—video frames for purposes of this discussion—such as those found in a television broadcast. Each video frame is divided into subregions called macro blocks, which each include one or more pixels. FIG. 1A is a 16-pixel-by-16-pixel macro block 30 having 256 pixels 32 (not drawn to scale). In the MPEG standards, a macro block is typically 16×16 pixels, although other compression standards may use macro blocks having other dimensions. In the original video frame, i.e., the frame before compression, each pixel 32 has a respective luminance value Y and a respective pair of color—, i.e., chroma—, difference values CB and CR.
Referring to FIGS. 1A–1D, before compression of the frame, the digital luminance (Y) and chroma-difference (CB and CR) values that will be used for compression, i.e., the pre-compression values, are generated from the original Y, CB, and CR values of the original frame. In the MPEG 4:2:0 format, the pre-compression Y values are the same as the original Y values. Thus, each pixel 32 merely retains its original luminance value Y. But to reduce the amount of data to be compressed, the MPEG 4:2:0 format allows only one pre-compression CB value and one pre-compression CR value for each group 34 of four pixels 32. Each of these pre-compression CB and CR values are respectively derived from the original CB and CR values of the four pixels 32 in the respective group 34. For example, a pre-compression CB value may equal the average of the original CB values of the four pixels 32 in the respective group 34. Thus, referring to FIGS. 1B–1D, the pre-compression Y, CB, and CR values generated for a macro block are arranged as one 16×16 matrix 36 of pre-compression Y values (equal to the original Y values for each respective pixel 32), one 8×8 matrix 38 of pre-compression CB values (equal to one derived CB value for each group 34 of four pixels 32), and one 8×8 matrix 40 of pre-compression CR values (equal to one derived CR value for each group 34 of four pixels 32). The matrices 36, 38, and 40 are often called “blocks” of values. Furthermore, because it is convenient to perform the compression transforms on 8×8 blocks of pixel values instead of on 16×16 blocks, the block 36 of pre-compression Y values is subdivided into four 8×8 blocks 42a–42d, which respectively correspond to the 8×8 blocks A–D of pixels in the macro block 30. Thus, referring to FIGS. 1A–1D, six 8×8 blocks of pre-compression pixel data are generated for each macro block 30: four 8×8 blocks 42a–42d of pre-compression Y values, one 8×8 block 38 of pre-compression CB values, and one 8×8 block 40 of pre-compression CR values.
FIG. 2 is a block diagram of an MPEG compressor 50, which is more commonly called an encoder. Generally, the encoder 50 converts the pre-compression data for a frame or sequence of frames into encoded data that represent the same frame or frames with significantly fewer data bits than the pre-compression data. To perform this conversion, the encoder 50 reduces or eliminates redundancies in the pre-compression data and reformats the remaining data using efficient transform and coding techniques.
More specifically, the encoder 50 includes a frame-reorder buffer 52, which receives the pre-compression data for a sequence of one or more frames and reorders the frames in an appropriate sequence for encoding. Thus, the reordered sequence is often different than the sequence in which the frames are generated and will be displayed. The encoder 50 assigns each of the stored frames to a respective group, called a Group Of Pictures (GOP), and labels each frame as either an intra (I) frame or a non-intra (non-I) frame. For example, each GOP may include three I frames and twelve non-I frames for a total of fifteen frames. The encoder 50 always encodes an I frame without reference to another frame, but can and often does encode a non-I frame with reference to one or more of the other frames in the GOP. The encoder 50 does not, however, encode a non-I frame with reference to a frame in a different GOP.
Referring to FIGS. 2 and 3, during the encoding of an I frame, the 8×8 blocks (FIGS. 1B–1D) of the pre-compression Y, CB, and CR values that represent the I frame pass through a summer 54 to a Discrete Cosine Transformer (DCT) 56, which transforms these blocks of values into respective 8×8 blocks of one DC (zero frequency) transform value and sixty-three AC (non-zero frequency) transform values. FIG. 3 is a block 57 of luminance transform values Y-DCT(0, 0)a–Y-DCT(7, 7)a, which correspond to the pre-compression luminance pixel values Y(0, 0)a–Y(7, 7)a in the block 36 of FIG. 1B. Thus, the block 57 has the same number of luminance transform values Y-DCT as the block 36 has of luminance pixel values Y. Likewise, blocks of chroma transform values CB-DCT and CR-DCT (not shown) correspond to the chroma pixel values in the blocks 38 and 40. Furthermore, the pre-compression Y, CB, and CR values pass through the summer 54 without being summed with any other values because the summer 54 is not needed when the encoder 50 encodes an I frame. As discussed below, however, the summer 54 is often needed when the encoder 50 encodes a non-I frame.
Referring to FIG. 2 and FIG. 4, a quantizer and zigzag scanner 58 limits each of the transform values from the DCT 56 to a respective maximum value, and provides the quantized AC and DC transform values on respective paths 60 and 62. FIG. 4 is an example of a zigzag scan pattern 63, which the quantizer and zigzag scanner 58 may implement. Specifically, the quantizer and scanner 58 reads the transform values in the transform block (such as the transform block 57 of FIG. 3) in the order indicated. Thus, the quantizer and scanner 58 reads the transform value in the “0” position first, the transform value in the “1” position second, the transform value in the “2” position third, and so on until it reads the transform value in the “63” position last. The quantizer and zigzag scanner 58 reads the transform values in this zigzag pattern to increase the coding efficiency as is known. Of course, depending upon the coding technique and the type of images being encoded, the quantizer and zigzag scanner 58 may implement other scan patterns too.
Referring again to FIG. 2, a prediction encoder 64 predictively encodes the DC transform values, and a variable-length coder 66 converts the quantized AC transform values and the quantized and predictively encoded DC transform values into variable-length codes such as Huffman codes. These codes form the encoded data that represent the pixel values of the encoded I frame. A transmit buffer 68 then temporarily stores these codes to allow synchronized transmission of the encoded data to a decoder (discussed below in conjunction with FIG. 6). Alternatively, if the encoded data is to be stored instead of transmitted, the coder 66 may provide the variable-length codes directly to a storage medium such as a CD-ROM.
If the I frame will be used as a reference (as it often will be) for one or more non-I frames in the GOP, then, for the following reasons, the encoder 50 generates a corresponding reference frame by decoding the encoded I frame with a decoding technique that is similar or identical to the decoding technique used by the decoder (FIG. 6). When decoding non-I frames that are referenced to the I frame, the decoder has no option but to use the decoded I frame as a reference frame. Because MPEG encoding and decoding are lossy—some information is lost due to quantization of the AC and DC transform values—the pixel values of the decoded I frame will often be different than the pre-compression pixel values of the original I frame. Therefore, using the pre-compression I frame as a reference frame during encoding may cause additional artifacts in the decoded non-I frame because the reference frame used for decoding (decoded I frame) would be different than the reference frame used for encoding (pre-compression I frame).
Therefore, to generate a reference frame for the encoder that will be similar to or the same as the reference frame for the decoder, the encoder 50 includes a dequantizer and inverse zigzag scanner 70, and an inverse DCT 72, which are designed to mimic the dequantizer and scanner and the inverse DCT of the decoder (FIG. 6). The dequantizer and inverse scanner 70 first implements an inverse of the zigzag scan path implemented by the quantizer 58 such that the DCT values are properly located within respective decoded transform blocks. Next, the dequantizer and inverse scanner 70 dequantizes the quantized DCT values, and the inverse DCT 72 transforms these dequantized DCT values into corresponding 8×8 blocks of decoded Y, CB, and CR pixel values, which together compose the reference frame. Because of the losses incurred during quantization, however, some or all of these decoded pixel values may be different than their corresponding pre-compression pixel values, and thus the reference frame may be different than its corresponding pre-compression frame as discussed above. The decoded pixel values then pass through a summer 74 (used when generating a reference frame from a non-I frame as discussed below) to a reference-frame buffer 76, which stores the reference frame.
During the encoding of a non-I frame, the encoder 50 initially encodes each macro-block of the non-I frame in at least two ways: in the manner discussed above for I frames, and using motion prediction, which is discussed below. The encoder 50 then saves and transmits the resulting code having the fewest bits. This technique insures that the macro blocks of the non-I frames are encoded using the fewest bits.
With respect to motion prediction, an object in a frame exhibits motion if its relative position changes in the preceding or succeeding frames. For example, a horse exhibits relative motion if it gallops across the screen. Or, if the camera follows the horse, then the background exhibits relative motion with respect to the horse. Generally, each of the succeeding frames in which the object appears contains at least some of the same macro blocks of pixels as the preceding frames. But such matching macro blocks in a succeeding frame often occupy respective frame locations that are different than the respective frame locations they occupy in the preceding frames. Alternatively, a macro block that includes a portion of a stationary object (e.g., tree) or background scene (e.g., sky) may occupy the same frame location in each of a succession of frames, and thus exhibit “zero motion”. In either case, instead of encoding each frame independently, it often takes fewer data bits to tell the decoder “the macro blocks R and Z of frame 1 (non-I frame) are the same as the macro blocks that are in the locations S and T, respectively, of frame 0 (reference frame).” This “statement” is encoded as a motion vector. For a relatively fast moving object, the location values of the motion vectors are relatively large. Conversely, for a stationary or relatively slow-moving object or background scene, the location values of the motion vectors are relatively small or equal to zero.
FIG. 5 illustrates the concept of motion vectors with reference to the non-I frame 1 and the reference frame 0 discussed above. A motion vector MVR indicates that a match for the macro block in the location R of frame 1 can be found in the location S of a reference frame 0. MVR has three components. The first component, here 0, indicates the frame (here frame 0) in which the matching macro block can be found. The next two components, XR and YR, together comprise the two-dimensional location value that indicates where in the frame 0 the matching macro block is located. Thus, in this example, because the location S of the frame 0 has the same X-Y coordinates as the location R in the frame 1, XR=YR=0. Conversely, the macro block in the location T matches the macro block in the location Z, which has different X-Y coordinates than the location T. Therefore, Xz and Yz represent the location T with respect to the location Z. For example, suppose that the location T is ten pixels to the left of (negative X direction) and seven pixels down from (negative Y direction) the location Z. Therefore, MVz=(0, −10, −7). Although there are many other motion-vector schemes available, they are all based on the same general concept. For example, the locations R may be bidirectionally encoded. That is, the location R may have two motion vectors that point to respective matching locations in different frames, one preceding and the other succeeding the frame 1. During decoding, the pixel values of these matching locations are averaged or otherwise combined to calculate the pixel values of the location.
Referring again to FIG. 2, motion prediction is now discussed in detail. During the encoding of a non-I frame, a motion predictor 78 compares the pre-compression Y values—the CB and CR values are not used during motion prediction—of the macro blocks in the non-I frame to the decoded Y values of the respective macro blocks in the reference I frame and identifies matching macro blocks. For each macro block in the non-I frame for which a match is found in the I reference frame, the motion predictor 78 generates a motion vector that identifies the reference frame and the location of the matching macro block within the reference frame. Thus, as discussed below in conjunction with FIG. 6, during decoding of these motion-encoded macro blocks of the non-I frame, the decoder uses the motion vectors to obtain the pixel values of the motion-encoded macro blocks from the matching macro blocks in the reference frame. The prediction encoder 64 predictively encodes the motion vectors, and the coder 66 generates respective codes for the encoded motion vectors and provides these codes to the transmit buffer 68.
Furthermore, because a macro block in the non-I frame and a matching macro block in the reference I frame are often similar but not identical, the encoder 50 encodes these differences along with the motion vector so that the decoder can account for them. More specifically, the motion predictor 78 provides the decoded Y values of the matching macro block of the reference frame to the summer 54, which effectively subtracts, on a pixel-by-pixel basis, these Y values from the pre-compression Y values of the matching macro block of the non-I frame. These differences, which are called residuals, are arranged in 8×8 blocks and are processed by the DCT 56, the quantizer and scanner 58, the coder 66, and the buffer 68 in a manner similar to that discussed above, except that the quantized DC transform values of the residual blocks are coupled directly to the coder 66 via the line 60, and thus are not predictively encoded by the prediction encoder 64.
In addition, it is possible to use a non-I frame as a reference frame. When a non-I frame will be used as a reference frame, the quantized residuals from the quantizer and zigzag scanner 58 are respectively dequantized, reordered, and inverse transformed by the dequantizer and inverse scanner 70 and the inverse DCT 72, respectively, so that this non-I reference frame will be the same as the one used by the decoder for the reasons discussed above. The motion predictor 78 provides to the summer 74 the decoded Y values of the reference frame from which the residuals were generated. The summer 74 adds the respective residuals from the inverse DCT 72 to these decoded Y values of the reference frame to generate the respective Y values of the non-I reference frame. The reference-frame buffer 76 then stores the reference non-I frame along with the reference I frame for use in motion encoding subsequent non-I frames.
Although the circuits 58 and 70 are described as performing the zigzag and inverse zigzag scans, respectively, in other embodiments, another circuit may perform the zigzag scan and the inverse zigzag scan may be omitted. For example, the coder 66 can perform the zigzag scan and the circuit 58 can perform the quantization only. Because the zigzag scan is outside of the reference-frame loop, the dequantizer 70 can omit the inverse zigzag scan. This saves processing power and processing time.
Still referring to FIG. 2, the encoder 50 also includes a rate controller 80 to insure that the transmit buffer 68, which typically transmits the encoded frame data at a fixed rate, never overflows or empties, i.e., underflows. If either of these conditions occurs, errors may be introduced into the encoded data stream. For example, if the buffer 68 overflows, data from the coder 66 is lost. Thus, the rate controller 80 uses feed back to adjust the quantization scaling factors used by the quantizer/scanner 58 based on the degree of fullness of the transmit buffer 68. Specifically, the fuller the buffer 68, the larger the controller 80 makes the scale factors, and the fewer data bits the coder 66 generates. Conversely, the more empty the buffer 68, the smaller the controller 80 makes the scale factors, and the more data bits the coder 66 generates. This continuous adjustment insures that the buffer 68 neither overflows or underflows.
FIG. 6 is a block diagram of a conventional MPEG decompresser 82, which is commonly called a decoder and which can decode frames that are encoded by the encoder 50 of FIG. 2.
Referring to FIGS. 6 and 7, for I frames and macro blocks of non-I frames that are not motion predicted, a variable-length decoder 84 decodes the variable-length codes received from the encoder 50. A prediction decoder 86 decodes the predictively decoded DC transform values, and a dequantizer and inverse zigzag scanner 87, which is similar or identical to the dequantizer and inverse zigzag scanner 70 of FIG. 2, dequantizes and rearranges the decoded AC and DC transform values. Alternatively, another circuit such as the decoder 84 can perform the inverse zigzag scan. An inverse DCT 88, which is similar or identical to the inverse DCT 72 of FIG. 2, transforms the dequantized transform values into pixel values. For example, FIG. 7 is a block 89 of luminance inverse-transform values Y-IDCT, i.e., decoded luminance pixel values, which respectively correspond to the luminance transform values Y-DCT in the block 57 of FIG. 3 and to the pre-compression luminance pixel values Ya of the block 42a of FIG. 1B. But because of losses due to the quantization and dequantization respectively implemented by the encoder 50 (FIG. 2) and the decoder 82 (FIG. 6), the decoded pixel values in the block 89 are often different than the respective pixel values in the block 42a. 
Still referring to FIG. 6, the decoded pixel values from the inverse DCT 88 pass through a summer 90—which is used during the decoding of motion-predicted macro blocks of non-I frames as discussed below—into a frame-reorder buffer 92, which stores the decoded frames and arranges them in a proper order for display on a video display unit 94. If a decoded frame is used as a reference frame, it is also stored in the reference-frame buffer 96.
For motion-predicted macro blocks of non-I frames, the decoder 84, dequantizer and inverse scanner 87, and inverse DCT 88 process the residual transform values as discussed above for the transform values of the I frames. The prediction decoder 86 decodes the motion vectors, and a motion interpolator 98 provides to the summer 90 the pixel values from the reference-frame macro blocks to which the motion vectors point. The summer 90 adds these reference pixel values to the residual pixel values to generate the pixel values of the decoded macro blocks, and provides these decoded pixel values to the frame-reorder buffer 92. If the encoder 50 (FIG. 2) uses a decoded non-I frame as a reference frame, then this decoded non-I frame is stored in the reference-frame buffer 96.
Referring to FIGS. 2 and 6, although described as including multiple functional circuit blocks, the encoder 50 and the decoder 82 may be implemented in hardware, software, or a combination of both. For example, the encoder 50 and the decoder 82 are often implemented by a respective one or more processors that perform the respective functions of the circuit blocks.
More detailed discussions of the MPEG encoder 50 and the MPEG decoder 82 of FIGS. 2 and 6, respectively, and of the MPEG standard in general are available in many publications including “Video Compression Demystified” by Peter D. Symes, McGraw-Hill, 2001, which is incorporated by reference. Furthermore, there are other well-known block-based compression techniques for encoding and decoding both video and still images.
DC Prediction in MPEG-4
Referring to FIG. 8, a macro block 100 typically includes four 8×8 luminance blocks 102A–102D. The macro block 100 also includes two or more 8×8 chrominance blocks that are omitted for clarity. Each macro block 100 is either an intra (I) or inter (P) macro block. An I macro block is not encoded/decoded using motion prediction, but may have coefficients that are DC/AC predicted with respect to another macroblock. Conversely, a P macroblock block is motion predicted. A P frame can have I macro blocks within it, but an I frame has no P macro blocks within it.
The first coefficient of each block 102A–102D is a DC (zero frequency) coefficient, and the next 63 coefficients are AC (non-zero frequency) coefficients. For example, the first coefficient DCA of the block 102A is a DC coefficient.
To compress the encoded bit stream that represents the frame that includes the macroblock 100, the DC coefficients of all I macro blocks (except the three upper-left-hand 8×8 blocks of the upper-left-hand macro block (not shown) of the frame) are prediction encoded. That is, each of the DC coefficients, such as DCA, of an I macro block are encoded as a residual value that equals the difference between the DC coefficient and either the DC coefficient from the block to the left or from the block to the top. For example, {overscore (DCA)}, which is the residual for DCA, equals (DCA–DCB) //QP102A(vertical prediction) or (DCA–DCC) //QP102A(horizontal prediction), where PQ102A is the quantization factor for the block 102A.
How one determines whether to use DCB (vertical prediction) or DCC (horizontal prediction) to predict DCA is discussed below.
The // operator is a special rounding-division operator defined by the MPEG-4 standard. Basically, if the value of DCB÷QP103B is positive, the // operator rounds the result to the nearest integer value. For example if DCB=13 and QP103B=3, 13÷3=4.333, and 13 // 3=4. If the result had been 4.5 or greater, // would round the result up to 5. For negative numbers, any number between and including −4.0 to −4.5 would round up to −4; any number less than −4.5 and greater than or equal to −5.0 would round down to −5.
The decoding, i.e., inverse prediction, of the DC coefficients such as DCA is done before the decoded coefficients in the block such as 2A are inverse quantized, i.e., multiplied by the quantization parameter for the macro block 100. Therefore, the desired predicted value of DCA is given by the following equation, where, for example purposes, we assume that vertical prediction has been used:DCA(not inverse quantized)={overscore (DCA)}+DCB//QP3B  (1)
{overscore (DCA)} is the decoded-but-not-inverse-quantized residual DC-coefficient value from the encoded MPEG-4 bit stream, and QP103B is the quantization parameter of the block 103B. Rounding division (//) of DCB by QP103B is necessary because DCB was previously inverse quantized, and thus must be requantized so that it has the same units—quantized units—as DCA, which has not yet been inverse quantized, i.e., not yet multiplied by QP102A (the quantization parameter of the block 102A).
One problem with the // operator is that calculating the result using a standard division operation followed by a standard rounding operation is time consuming in terms of the number of processor cycles required.
DC Scalar
The quantization parameter QP (such as QP103B in equation (1)) for each block is actually a pointer to a DC scalar, which can have more bits than QP. Because QP is transmitted in the encoded bit stream, it is desired that QP have as few bits as possible.
More specifically, the MPEG-4 standard defines QP as having a value from 1 to 31, and thus as being 5 bits long. The value of QP and the DC scalar for luminance and chrominance values are related according to Table I.
TABLE IQP1–45–89–2526–31luminanceDC Scalar82 × QPQP + 82 × QP − 16chrominanceDC Scaler8(QP + 13)/2QP − 6Range Of Values For The DC Coefficients
Each DC coefficient (such as DCA) has a value ranging from −2048 to +2047 before it is inverse quantized, i.e., multiplied by the DC scalar. The value of the inverse-quantized (i.e., post multiplication by DC scalar) DC coefficient is in the range (44×(−2048)) to (44×(+2047)).
AC Prediction
FIG. 9 shows the DC coefficients and two rows and two columns of AC coefficients for the 8×8 blocks 102A, 103B, and 103C of FIG. 8. As discussed above in conjunction with FIG. 8, each of these blocks has a total of 64 coefficients, a DC coefficient in the upper left-hand corner and 63 AC coefficients. For I macro blocks, the AC coefficients are prediction encoded and decoded in a manner similar to that described above for DC prediction. But as discussed in more detail below, one difference between AC and DC prediction is that AC prediction is done post inverse quantization. That is, AC prediction is done after the decoded, quantized AC coefficients in the surrounding blocks as well as the quantized AC prediction values in the block being processed have been multiplied by the step-sized quantization parameter QPAC, which is discussed below.
Still referring to FIG. 9, each of the AC coefficients is predicted either vertically or horizontally (in the same direction as the DC prediction) with the same element in the corresponding block. For example, assume that the AC coefficients in the block 102A are vertically predicted from the AC coefficients in the block 103B. In this case, AC coefficient AC102A1 in the block 102A is predicted from AC103B1 in the block 103B, and so on, according to the following equation:QF102A[i]=PredictQF102A[i]+(QF103B[i]×QP103B)//QP102A  (2)
where QF102A[i] is the inverse-quantized AC coefficient for element i of the block 102A, PredictQF102A[i] is the quantized AC prediction value for the element i, QF103B[i] is the quantized AC coefficient for the element i of the block 103B, QP103B is the AC quantization parameter for the block 103B, and QP102A is the AC quantization parameter for the block 102A. During encoding of the block 102A, Prediction Value, the precursor of PredictQF102A[i], is calculated according to the following equation:PredictQF102A[i]−QF103B[i]/QP103B=Prediction Value  (3)
During decoding of the block 102A but before application of equation (2), QF102A[i]/QP102A and Prediction Value are multiplied by QP102A (i.e., are inverse quantized) to give QF102A[i] and PredictQF102A[i]=QP102A×Prediction Value, and QF103B[i]/QP103B is multiplied by QP103B (i.e., inverse quantized) to give QF103B[i]. Substituting these values in equation (3) and rearranging the values gives the following equation:(QF102A[i]/QP102A)×QP102A=(Prediction Value)×QP102A+(QF103B[i]/QP103B)×QP102A  (4)Because QF102A[i], PredictQF102A[i], and QF103B are already available, we multiply QF103B by QP102A and round divide (//) by QP103B, which gives equation (2).
Again, because the MPEG-4 defined rounding division // operator is complicated and requires many processor clock cycles, it would be desirable to eliminate this division from equation (2) to simplify and speed up the block decoding process.
AC Step-sized Value
As discussed above for the DC quantization parameter QP, the AC quantization parameter QP is a pointer to a step-sized value that is used in the equations (2)–(4) in place of QP102A and QP103B.
More specifically, The AC QP is a 5-bit number having a value from 1 to 31, and the AC step-sized value to which QP points equals 2×QP for all values of QP.
Range Of Inverse-quantized AC Coefficient Values
The range of the inverse-quantized AC coefficients QF in equations (2)–(4) is −2048 to +2047.